ok when you go into paint skin weights you want to select the mesh of your model, aka the teeth.
In your component editor go under the smooth skins tab.
Down the left it should have your mesh name and then all your vertices below it in Numbered order. In my image you can see how each verticy is influenced by what bone (bones are labeled across the columns).
Now it takes a bunch of tweaking but you will want to change the influence values for your verts to get them to work properly, but for you i think a simple solution is very easy.

If say vertex 210-245 are your upper teeth than you would select them, and find the bottom jaw bones and zero out the influence. When you move the bottom jaw afterwards you should see no movement in the upper teeth.
I hope that helps!